GPS Triangulation problem?

Question

If a point is 390 feet from N33* 30.674 W 88* 29.450, 791 feet from N 33* 30.711 W 88* 29.229, and 773 feet from N33* 30.836 W88* 29.407, where is the point? Thanks!
Format is dd mm.mmm Datum is WGS84 if that matters.

Answer 1

To an accuracy of +/- 0.001 minutes, the answer is N 33 30.709 W 88 29.385.

I solved it graphically using GPS Visualizer. I converted the coordinates to decimal degrees and used GPS Visualizer to generate range rings (first URL below). Then I copied all the range ring data points and pasted it into GPS Visualizer to create a Google Map (second URL below).

I saved all the data points online (third URL below). To see the Google Map with the solution, copy the third URL. Go to GPS Visualizer at the second URL. On the bottom right of the page where it says "Or provide the URL of data on the Web", paste in the third URL. Then press the "Draw the map" button.

I have checked the answer with NGS software (fourth URL below) and the maximum deviation from the distances is 5.3 feet. That is much better than the accuracy of the typical handheld GPS receiver.

If you are looking for a mathematically exact solution, I don't think there is one. If you zoom in on the intersection, you'll see that the circles do not meet exactly at one point. Since 0.001 minutes at that latitude is a distance of 6.1 feet, it's not surprising that the given coordinates and distances are not accurate enough for a mathematically exact solution.

If this is for some sort of contest, do I get a share of the prize? :)

Answer 2

Over those distances, the Earth is flat. Draw it out on graph paper.
Draw circle around each point.

Be sure to figure that E-W latitude increments are not the same distance as N-S.